scholarly journals Fractional electromagnetic waves in plasma and dielectric media with Caputo generalized fractional derivative

2020 ◽  
Vol 66 (6 Nov-Dec) ◽  
pp. 848
Author(s):  
N. Bhangale ◽  
K. B. Kachhia
Keyword(s):  
Wave Equation ◽  
Fractional Derivative ◽  
Electromagnetic Fields ◽  
Electromagnetic Waves ◽  
Analytic Solution ◽  
Dielectric Media ◽  
Fractional Differential ◽  
Fractional Orders ◽  
Generalized Fractional Derivative ◽  
Space Wave

The wave equation has very significance role in many area of physics. The paper addresses thesolution of fractional differential equations of electromagnetic wave in plasma and dielectric media with Caputo generalized fractional derivative. The ρ−Laplace transform introduced by Fahd and Thabet was used to obtain the analytic solution of fractional differential equation which arising in electromagnetic fields. We investigate that the wave equation in fractional space can effectively describe the behaviour of space wave and time wave. The results show that the electromagnetic fields change with different fractional orders.

scholarly journals Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 94 ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Kamal Shah ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet ◽  
...  
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Integral Condition ◽  
Hilfer Fractional Derivative ◽  
Fractional Differential ◽  
Generalized Fractional Derivative ◽  
Stability Results

This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer’s and Banach fixed point theorems. In addition, the Ulam-Hyers and generalized Ulam-Hyers stability of the problem are established. Finally, some examples are given to illustrative the results.

scholarly journals ANALYSIS OF DENGUE FEVER OUTBREAK BY GENERALIZED FRACTIONAL DERIVATIVE

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040038
Author(s):  
PAUL BOSCH ◽  
J. F. GÓMEZ-AGUILAR ◽  
JOSÉ M. RODRÍGUEZ ◽  
JOSÉ M. SIGARRETA
Keyword(s):  
Fractional Derivative ◽  
Dengue Fever ◽  
Gaussian Model ◽  
Integral Operators ◽  
Real Data ◽  
Practical Application ◽  
Gaussian Models ◽  
Fractional Differential ◽  
Generalized Differential ◽  
Generalized Fractional Derivative

In this paper, we use the generalized fractional derivative in order to study the fractional differential equation associated with a fractional Gaussian model. Moreover, we propose new properties of generalized differential and integral operators. As a practical application, we estimate the order of the derivative of the fractional Gaussian models by solving an inverse problem involving real data on the dengue fever outbreak.

scholarly journals Stability of solutions for generalized fractional differential problems by applying significant inequality estimates

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammed D. Kassim ◽  
Thabet Abdeljawad ◽  
Saeed M. Ali ◽  
Mohammed S. Abdo
Keyword(s):  
Fractional Derivative ◽  
Power Function ◽  
Sufficient Conditions ◽  
Research Paper ◽  
Stability Of Solutions ◽  
Initial Value ◽  
Regularization Techniques ◽  
Fractional Differential ◽  
The Stability ◽  
Generalized Fractional Derivative

AbstractIn this research paper, we intend to study the stability of solutions of some nonlinear initial value fractional differential problems. These equations are studied within the generalized fractional derivative of various orders. In order to study the solutions’ decay to zero as a power function, we establish sufficient conditions on the nonlinear terms. To this end, some versions of inequalities are combined and generalized via the so-called Bihari inequality. Moreover, we employ some properties of the generalized fractional derivative and appropriate regularization techniques. Finally, the paper involves examples to affirm the validity of the results.

Atangana-Baleanu fractional derivative applied to electromagnetic waves in dielectric media

2016 ◽  
Vol 30 (15) ◽  
pp. 1937-1952 ◽  
Author(s):  
J. F. Gómez-Aguilar ◽  
R. F. Escobar-Jiménez ◽  
M. G. López-López ◽  
V. M. Alvarado-Martínez
Keyword(s):  
Fractional Derivative ◽  
Electromagnetic Waves ◽  
Dielectric Media

scholarly journals A study of symmetric contractions with an application to generalized fractional differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Aftab Hussain ◽  
Fahd Jarad ◽  
Erdal Karapinar
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fractional Differential ◽  
Generalized Fractional Derivative ◽  
Fractional Boundary Value Problems

AbstractThis article proposes four distinct kinds of symmetric contraction in the framework of complete F-metric spaces. We examine the condition to guarantee the existence and uniqueness of a fixed point for these contractions. As an application, we look for the solutions to fractional boundary value problems involving a generalized fractional derivative known as the fractional derivative with respect to another function.

scholarly journals Analytic Solution for theRLElectric Circuit Model in Fractional Order

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
P. V. Shah ◽  
A. D. Patel ◽  
I. A. Salehbhai ◽  
A. K. Shukla
Keyword(s):  
Differential Equation ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Analytic Solution ◽  
Electrical Circuit ◽  
Special Cases ◽  
The Laplace Transform ◽  
Fractional Differential

This paper provides an analytic solution ofRLelectrical circuit described by a fractional differential equation of the order0<α≤1. We use the Laplace transform of the fractional derivative in the Caputo sense. Some special cases for the different source terms have also been discussed.

scholarly journals Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1866
Author(s):  
Mohamed Jleli ◽  
Bessem Samet ◽  
Calogero Vetro
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
A Priori Estimates ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Higher Order ◽  
Differential Inequalities ◽  
Structure Of Solutions ◽  
Nonlinear Capacity ◽  
Fractional Differential

Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis of the integral form of the inequality with appropriate choice of test function.

Sign in / Sign up

Export Citation Format

Share Document